Group classification of a class of equations arising in financial mathematics

We provide a group classification of a class of nonlinearisable evolution partial differential equations which arise in Financial Mathematics. Sixteen different cases are identified for the general problem and another seven for a restricted version. In the cases for which the algebra is suitable we determine the solution to the problem u(0,x)=U, where U is a constant. In addition we provide a number of solutions based upon reduction using inequivalent subalgebras.